"What we should probably do is go and split up investment banking from banking, have banks be deposit takers, have banks make commercial loans and real estate loans, have banks do something that's not going to risk the taxpayer dollars, that's not too big to fail," Weill told CNBC. "If they want to hedge what they're doing with their investments, let them do it in a way that's going to be mark-to-market so they're never going to be hit."

They should be broken up, said Weill, "so that the taxpayer will never be at risk, the depositors won't be at risk, the leverage of the banks will be something reasonable..."

"Weill helped engineer the 1998 merger of Travelers Group Inc. and Citicorp, a deal that required repeal of the Depression-era Glass-Steagall law that forced deposit-taking companies backed by government insurance to be separate from investment banks. The New York-based company became the biggest lender in the world before almost failing and taking a $45 billion taxpayer bailout in 2008."

"He and his institution were in the lead in pushing for the repeal of Glass-Steagall and then, of course, Citigroup is the poster child for too-big-to-fail in the bailouts during the 2008 crisis," Bair said. "It is truly ironic."

After the Weill interview, CNBC also talked to Bethany McLean, who writes for Reuters. She called Weill's comments "astonishing."

Here's video of that interview:

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